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## Bug's Eye 7

You are a bug sitting in one corner of a cubic room. You wish to walk (not fly) to the extreme opposite corner – the corner furthest from you. Describe the shortest path that you can walk.

See explanation.

Refer to the diagram.

The problem phrased differently is that we have to get from point A to point B only moving along the walls.

The shortest route is shown it is A-H-B where H is the mid point of D-E.

The length of this route can easily be calculated, assume the cube has sides of length 1 unit (it doesn’t matter what these units are, meters, feet, what ever) The distance A-H is the hypotenuse of a triangle 1 x ½ a quick bit of pythag tells us that A-H equals sqrt(5/4). Similarly H-B has the same length hence the total length is 2 x sqrt(5/4) this is actually equal to the square root of 5

A-H-B = sqrt(5) = 2.236

Some people think the shortest root is A-C-B or A-E-B or A-F-B etc. (they are all the same) this has a length of 1 + sqrt(2) ie. about 2.414.

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Anjali Gola

A to G then G to B

Hell lover

Its the same as A-C-B or A-E-B or A-F-B etc..

jmander

Would be harder if the red line in the diagram didn't give it away.

Jay Elliott

Agreed. I think the same diagram without the red path would be ideal.

leilei3915

2018529 leilei3915

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